## Communications in Mathematical Sciences

- Commun. Math. Sci.
- Volume 6, Number 4 (2008), 869-880.

### Vanishing viscosity and the accumulation of vorticity on the boundary

#### Abstract

We say that the vanishing viscosity limit holds in the classical sense if the velocity for a solution to the Navier-Stokes equations converges in the energy norm uniformly in time to the velocity for a solution to the Euler equations. We prove, for a bounded domain in dimension 2 or higher, that the vanishing viscosity limit holds in the classical sense if and only if a vortex sheet forms on the boundary.

#### Article information

**Source**

Commun. Math. Sci., Volume 6, Number 4 (2008), 869-880.

**Dates**

First available in Project Euclid: 18 December 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.cms/1229619674

**Mathematical Reviews number (MathSciNet)**

MR2511697

**Zentralblatt MATH identifier**

1161.76012

**Subjects**

Primary: 76D05: Navier-Stokes equations [See also 35Q30] 76B99: None of the above, but in this section 76D99: None of the above, but in this section

**Keywords**

Vanishing viscosity incompressible fluid mechanics

#### Citation

Kelliher, J. P. Vanishing viscosity and the accumulation of vorticity on the boundary. Commun. Math. Sci. 6 (2008), no. 4, 869--880. https://projecteuclid.org/euclid.cms/1229619674